In the Euthyphro, how does Socrates present two arguments to prove that the pious and the god-beloved are not the same?

I'll address the basic arguments in Euthyphro concerning the failure of "loved by the gods" to be an adequate definition of piety.

The first, and somewhat weaker, argument against the adequacy of this definition is that the gods disagree about many things. For example, Artemis approves of celibacy and Aphrodite abhors it. The gods supported opposite sides in the Trojan war. The gods are often portrayed as squabbling among themselves. Thus piety cannot be defined as what the gods love; they love many different things.

This argument is countered by the modified assertion that that piety has to do with what is beloved universally by all the gods. This is countered in turn by a more philosophically complex argument, namely one of causation, that leads us to an aporia. This complex argument is based on the problem of whether the gods love things because they are pious or whether divine love imbues things with piety. The former, however, means that we still have not located a definition of piety, because we have not yet listed a set of criteria defining the essence of piety, but have only described the way the gods react to it. 

How do ideas in Macbeth surrounding superstition, ambition and the difference between appearance and reality reveal human nature?

Macbeth's superstitious belief in the fate which the Weird Sisters have predicted for him, his incredible and violent ambition, and his failure to discern the difference between appearances and reality show just how easily human nature can be corrupted, especially when these factors combine.  If Macbeth had chalked the Weird Sisters' words up to the fantastic ramblings of a bunch of odd old women and never ambitiously dreamed of the life of which they spoke to him, he would probably be at home in Glamis, happy with his loving wife.  However, Macbeth allowed his ambition to run away with him, and it kept him from being able to see that things are not always as they seem, or put another way, that appearances can be deceiving.  It doesn't take much to turn a good man into a bad one, and this shows how easily corruptible human nature can be.

Why does To Kill a Mockingbird allude to the Civil War?

The novel alludes to that war a few times: in Chapter 9 (which we'll focus on), in Chapter 13, when it's briefly mentioned that Maycomb was "ignored" during the war, and in Chapter 28, when we see kids wearing all kinds of costumes, including Confederate hats.

It's pretty clear that the allusion from Chapter 9 is the most important. Why is it there?

By drawing a comparison between the Civil War and the current conflict between Atticus and the townspeople who want to convict Tom unfairly, the narrator helps us understand, first of all, the full extent of the seriousness of Tom's case.

Through that allusion, we also understand how the sentiments that fueled the Civil War are still affecting race relations in the South when this story takes place. Racism is still alive and kicking, and it's just as ugly as it was during the Civil War.

Finally, as Atticus explains the difference between the real war and the current conflict, the allusion helps us see that the conflict between Tom's supporters (mostly just Atticus and his kids) and Tom's haters is serious and yet perhaps not serious enough to tear apart friendships or families, like the Civil War did.

For reference, here is the full context of that allusion from Chapter 9:

“Simply because we were licked a hundred years before we started is no reason for us not to try to win,” Atticus said.

“You sound like Cousin Ike Finch,” I said. Cousin Ike Finch was Maycomb County’s sole surviving Confederate veteran. He wore a General Hood type beard of which he was inordinately vain. At least once a year Atticus, Jem and I called on him, and I would have to kiss him. It was horrible. Jem and I would listen respectfully to Atticus and Cousin Ike rehash the war. “Tell you, Atticus,” Cousin Ike would say, “the Missouri Compromise was what licked us, but if I had to go through it agin I’d walk every step of the way there an‘ every step back jist like I did before an’ furthermore we’d whip ‘em this time… now in 1864, when Stonewall Jackson came around by—I beg your pardon, young folks. Ol’ Blue Light was in heaven then, God rest his saintly brow…”

“Come here, Scout,” said Atticus. I crawled into his lap and tucked my head under his chin. He put his arms around me and rocked me gently. “It’s different this time,” he said. “This time we aren’t fighting the Yankees, we’re fighting our friends. But remember this, no matter how bitter things get, they’re still our friends and this is still our home.”

What does Atticus have to lose by defending Tom Robinson in To Kill a Mockingbird by Harper Lee?

Atticus has his good standing with the white community to lose. His business may be lost, and his political position in Montgomery taken from him.

When the leading townsmen stand in the Finch yard on the Sunday before the Tom Robinson is moved to the jailhouse, they have come to warn Atticus about the Old Sarum bunch. Atticus tries to allay their fears, but Link Deas says to Atticus,

'--don't see why you touched it in the first place,...You've got everything to lose from this Atticus. I mean everything. (Ch. 15)

Before the trial begins, the Idler's Club sits outside the courthouse and speak of the forthcoming trial. One of them comments, "...thinks he knows what he's doing." Another objects, "...you know the court appointed him to defend this nigger."
The other retorts, "Yeah, but Atticus aims to defend him. That's what I don't like about it."

Atticus's earnest defense of Tom Robinson is tantamount to acting like a "Yankee." For, in the Jim Crow South of the 1930's no white man defended the actions or supposed actions of a Negro. This is why the jury votes as it does. For Atticus to treat Tom as he would a white man is unheard of in Maycomb. Clearly, Atticus takes a huge risk by following his conscience.

In Catch-22, what is the balance of power between Yossarian and the chaplain?

Catch-22 opens with Yossarian’s reaction to meeting the chaplain:

It was love at first sight.

The first time Yossarian saw the chaplain he fell madly in love with him.

One might imagine that, due to the chaplain's status as a religious man and Yossarian's lovestruck state of mind, the balance of power would favor the chaplain. But contrary to the expectation of love at first sight, Yossarian describes his first impression as such:

Yossarian had no idea who he was and just took it for granted that he was either another doctor or another madman.

When under the impression that the chaplain is merely another officer, Yossarian is dismissive; however, upon realizing that the captain was also a chaplain, he is "astonished" and ecstatic. He is described as “[glowing] with affection” toward the chaplain, and calls him “sweet” after the chaplain had left. Perhaps the most telling line is this:

Yossarian wanted to help him.

In the first chapter, the balance of power clearly favors Yossarian. Although Captain Tappman is of equal rank and a chaplain as well, Yossarian feels himself superior to the chaplain and attempts to help him. Just as tellingly, the chaplain is described as flushing and blushing frequently throughout the encounter. His innocence is prominent: he "beamed gratefully" after Yossarian said he could visit him in the hospital.

Later in the book, the chaplain finds himself under Yossarian's protection. He sits with Yossarian and Dunbar at the officers club and feels safe, which he does not when alone. When Colonel Cathcart tries to throw him out, Yossarian "[rises] truculently to intervene" to throw an "avenging punch." 

As he is "sincerely a very helpful person who was never able to help anyone," the chaplain finds himself torn. He wants nothing more than to live quietly and return to his family, but he feels a sense of obligation to Yossarian. His attempt to talk to Major Major about the escalating number of missions fails; he believes himself to be the butt of a practical joke and with a "pleading whimper" escapes out the window. Particularly in comparison to Yossarian, who is, paradoxically, a brave coward, the chaplain appears far less resolved even as he attempts to aid him.

For all of his trepidation, the chaplain steps up when it is called for. Under suspicion of censoring letters under the name of Washington Irving, he recognizes Yossarian's handwriting and nonetheless refuses to give up his friend. After being punished for infractions he had never committed and accused of ridiculous crime, he is found guilty and told not the leave the island; in a "temper of scalding and vindictive resentment," he resolves to push the matter of the ever-growing number of missions. Though his attempt fails, it is growth regardless: the balance of power shifts in the chapter when the chaplain takes the fall for Yossarian and pushes for what is right.

In the hospital, the chaplain and Yossarian converse more as equals. The chaplain still blushes awkwardly, but Yossarian appears to value his opinion even though the chaplain didn't influence his decision: he had already planned not to take Cathcart and Korn's deal.

In the end, it is the chaplain's news that Orr has been washed ashore in Sweden that gives Yossarian the final push to leave. Yossarian, recognizing that Orr set up his escape deliberately, is jubilant; he calls on the chaplain to "for once in your life, succeed at something" and get him his uniform so that he can escape. Bolstered by Yossarian's confidence, the chaplain resolves to persevere in the face of Cathcart and Korn.

The power imbalance between Yossarian and the chaplain never reverses—Yossarian holds more sway throughout the relationship—but they both ultimately benefit from their friendship. While the chaplain is rarely able to aid Yossarian despite his dearest wishes to do so, he ultimately provides the catalyst for his escape; in turn, Yossarian gives him the gift of perseverance.

How does Sherlock Holmes use deductive reasoning to learn about Mr. Wilson in The Red-Headed League by Arthur Conan Doyle?

In The Red-Headed League, Sherlock Holmes and John Watson are hired by Mr. Jabez Wilson to look into the mysterious disappearance of a business known as the Red-Headed League. Upon being visited by Mr. Wilson, Sherlock Holmes announces that he knows Mr. Wilson has worked as a manual laborer, uses snuff tobacco, is a Freemason, has been working at writing, and has spent time in China. How could he possibly know such things if he is meeting Mr. Wilson for the first time? Mr. Holmes' career is built upon his talent for deductive reasoning-- the ability to observe his surroundings (including people) and make connections between the facts before him and the events which may have preceded.

For starters, Mr. Holmes has deduced by the fact that the muscles of Mr. Wilson's right hand are much larger than those in his left, that he has worked in manual labor. The exercise to his right hand resulted in greater muscle development. He has also discerned from the distinctive pin on Mr. Wilson's jacket that he is a member of the Freemasons. The "arc and compass," also called "Square and Compass," is a symbol used by the Freemasons. Mr. Holmes notices that the sleeve of Mr. Wilson's jacket has been worn down from writing and the repetitive motion of his wrist and elbow across the surface of a desk. Finally, Mr. Holmes recognizes a style of tattoo on Mr. Wilson which is unique to China. He does not tell us how he knows Mr. Wilson uses snuff tobacco, but if you are familiar with the other Sherlock Holmes stories, one can presume he noticed a staining on the fingers Mr. Wilson used to pinch out his tobacco. In each case, Mr. Holmes has observed the facts in front of him and worked out their most probable causes.

What did Mr. Hooper do when his veil swung forward while bending over the coffin? What did an observer say happened then?

When Mr. Hooper leans over the coffin of the dead maiden, his veil falls away from his face so that, if she were alive she would be able to see his face beneath the veil.  The narrator says that Mr. Hooper "hastily caught [it] back," meaning that he quickly grabbed the veil and pulled it back toward his face so that his face would not be revealed to the young woman's body inside the coffin.  

An old woman who witnessed this moment swears that in the instant when the maiden would have been able to glimpse the minister's face beneath his veil, "[her] corpse had shuddered," lightly rustling the maiden's cap and death shroud, though her face never moved or indicated any change.  However, it was only this one superstitious old woman that actually claims to have observed this interaction, and so it is not widely credited as truth.